British peace campaigner Tom Hurndall, 22, died on Tuesday after lying in a coma for nine months.
He was shot in April last year in the Gaza Strip while escorting Palestinian civilians to safety during a clash.
The Israeli authorities on Monday charged an Israeli soldier with grievous bodily harm over the shooting and said he would stand trial. Security sources said the charges would probably be changed to manslaughter since Hurndall's death.
A British coroner has asked police to assist in a British inquiry into the activist's death, a police spokeswoman said.
Hurndall's family, which believes the Israeli soldier shot the activist with the intention to kill, welcomed the news.
Tom's mother Jocelyn Hurndall told BBC Radio she was sceptical of Israel's intention to bring those responsible for the shooting to justice and condemned a "culture of impunity" in the Israeli army.
Calls for accountability
Arafat called Hurndall
a 'Palestinian martyr'
She said the family would press the government "to ensure that this soldier and other soldiers involved in the killing or the conspiracy to cover up the evidence stand trial, all the way up the chain of command".
Hurndall's supporters say he was wearing a bright orange jacket and helping Palestinian children cross a street under fire in the Gaza Strip town of Rafah when he was shot.
The soldier initially said he had opened fire on a man armed with a pistol, but later "admitted to firing in proximity to an unarmed civilian as a deterrent", the Israeli military has said.
"There's no question in our minds that this was a shot intended to kill," Jocelyn Hurndall said.
Palestinians honour Hurndall
His death sparked protests on Friday as about 100 Palestinian children and teenagers demonstrated in Rafah in his memory.
The demonstrators laid a wreath at the spot where Hurndall was fatally shot.
Four foreign peace activists also took part in the march, carrying photos of Hurndall and banners in English and Arabic denouncing his death.
On Thursday, Palestinian leader Yasir Arafat bestowed on him the status of a "Palestinian martyr".